In Mrs. Bramson's bedroom, Danny tucks in Mrs. Bramson and leaves, closing the bedroom door with an audible click. The next scene shows Danny outside the bedroom again closing the still-open door.
While Olivia and Justin are talking at the cricket match, in the background you see the couple with the dog start to walk by twice.
When Danny brings Mrs. Bramson inside after greeting the people who have come to gawk at the murder scene, Olivia is sitting at the desk using scissors. As Danny leaves to make tea, in the medium shot Olivia's arms are resting separately on the desk, but when the shot switches to a closeup, her hands are suddenly together, and her arms are propped on her elbows.
It is simply impossible to whistle when you have a cigarette in your mouth.
Wouldn't Olivia be charged as an accessory after the fact for deceiving the inspector about the contents of the hatbox? That lie not only facilitated Danny's first murder but also gave him opportunity to murder Mrs. Bramson.